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This work is supported by the Science and Technology Facilities Council (STFC), UK, US Department of Energy, Office of Nuclear Physics, under Contract No. DEAC02-06CH11357 and DE-FG02-94ER40834, NSF grant PHY-1404442.

High-spin states with the seniority v ≥ 2 have been investigated in the neutron-rich 118,120,122,124,126Sn isotopes. They were produced in fusion-fission processes following 48Ca + 208Pb, 48Ca + 238U reactions and via fission of target nuclei in the 64Ni + 238U system. By employing techniques of delayed- and cross-coincidences, it was possible to establish level schemes up to an 8 MeV excitation energy. The 13− and 15− states were identified as being isomeric and their half-lives were determined. The reduced transition probabilities extracted for isomeric transitions behave very regularly with the mass number A. The spin-parity values assigned to or suggested for the identified states were supported by shell-model calculations and by systematics.

We discuss the problem of estimating uncertainties of the physical theories while keeping in mind the applications to nuclear structure. We present an analytical model which illustrates the present-day difficulties in achieving a satisfactory level of predictive power in nuclear structure theories as well as suggests the most important direction of improvements, required first of all on the level of the associated solution of the inverse problem of applied mathematics—as explained and illustrated in some detail in the text.

Gamma rays in the π−2ν2 nucleus 208Hg and π−1ν2 nucleus 209Tl have been studied at Gammasphere using deep-inelastic reactions induced by a 1360 MeV208 Pb beam on a thick 238U target. Previously unknown yrast γ-ray cascades above the 8+ and 17/2+ nanosecond isomers in 208Hg and 209Tl, respectively, were identified in coincidence with known γ rays deexciting the isomers. Yrast levels up to spin 13− in 208Hg have been located, and they are interpreted in light of the structure of the 210Pb isotone and with the help of shell model calculations. Shell model calculations by using the Vlow–k realistic interaction have been performed for 210Pb and 208Hg, and compared with experiment. The Vlow–k effective Hamiltonian seems to account well for the properties of these neutron-rich shell model nuclei.

In this and the follow-up article we briefly discuss what we believe represents one of the most serious problems in contemporary nuclear structure: the question of statistical significance of parametrizations of nuclear microscopic Hamiltonians and the implied predictive power of the underlying theories. In the present Part I, we introduce the main lines of reasoning of the so-called Inverse Problem Theory, an important sub-field in the contemporary Applied Mathematics, here illustrated on the example of the Nuclear Mean-Field Approach.